circuit question

imagine you have 2 cells and 2 bulbs in series, the 2 bulbs at bottom and 2 cells at top. Then you attach a wire with a bulb in the middle in between the 2 cells and 2 bulbs. Why does this bulb then not turn on? I know its because no current flows down through it but why? thanks

https://www.physics.ox.ac.uk/system/files/file_attachments/pat-2006.pdf Q11 d

Reply 1

Ferret!

Treat the circuit as two halves that share the same centre blub. The currents I_a and I_b flow in opposite directions through the blub (see diagram). As these two circuits share otherwise identical components, I_a = I_b through that central bulb, so I_TOT = 0.

For why the bulb does not turn on (i.e. show no luminosity, L), we can use the relation